Is it muter to take a fruit or vegetable (like an Avocado) and put it into a nylon bag on Shabbos in order it should get softer?
This does not appear to involve any problem, provided it is being done for Shabbos–meaning that by the end of Shabbos it might be soft enough to be eaten.
Although there is some discussion among poskim concerning rendering an inedible food edible on Shabbos (though the conclusion of the Biur Halachah 318 is that there is no makeh be-patish for foods), in this case the food is edible before, and making it softer only improves it. There is therefore no problem.
If it certainly won’t become soft enough to eat on Shabbos, placing the fruit in a bag will involve a problem of hachanah, preparing for the weekday.